Some Cyclo-quaternionic Lattices

Journal of Algebra

Volumn 199, Issue 2, 1998, Pages 472-498

  Nebe, Gabriele ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039758270     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.1997.7163     Document Type: Article

References (26)

1. Bachoc C., Batut C. Etude Algorithmique de Réseaux Construits avec la Forme Trace. Experimental Math. 1:1992;183-190.
2. Bayer-Fluckiger E. Definite unimodular lattices having an automorphism of given characteristic polynomial. Comment. Math. Helv. 59:1984;509-538.
3. Blichfeldt H. F. The minimum values of positive quadratic forms in six, seven and eight variables. Math. Z. 39:1935;1-15.
4. f). J. Algebra. 40:1976;75-96.
5. Conway J. H., Sloane N. J. A. Sphere Packings, Lattices and Groups. 1988;Springer-Verlag, New York/Berlin.
6. Curtis C. W., Reiner I. Methods of Representation Theory with Applications to Finite Groups and Orders. 1981;Wiley, New York.
7. Dornhoff L. Group Representation Theory. Pure and Applied Mathematics. 1972;Dekker, New York.
8. Feit W. The Representation Theory of Finite Groups. 1982;North-Holland, Amsterdam.
9. Feit W. The computations of some Schur indices. Israel J. Math. 46:1983;274-300.
10. Gross B. H. Group representations and lattices. J. Amer. Math. Soc. 3:1990;929-960.
11. Lang S. Introduction to Modular Forms. Grundlehren der Mathematischen Wissenschaften. 1976;Springer-Verlag, New York/Berlin.
12. H. Napias, Etude expérimentale et algorithmique de réseaux euclidiens, 1996.
13. G. Nebe, Finite quaternionic matrix groups.
14. Nebe G., Plesken W. Finite rational matrix groups of degree 16. Mem. Amer. Math. Soc. 116:1995.
15. Batut C., Bernardi D., Cohen H., Olivier M. PARI-GP 1.39. 1995;Université Bordeaux I.
16. Plesken W. Group Rings of Finite Groups over thep. Lecture Notes in Mathematics. 1983;Springer-Verlag, New York/Berlin.
17. Plesken W., Nebe G. Finite rational matrix groups. Mem. Amer. Math. Soc. 116:1995.
18. Plesken W., Souvignier B. Computing isometries of lattices. J. Symbolic Comput. 24:1997;327-334.
19. Quebbemann H.-G. Modular lattices in Euclidean Spaces. J. Number Theory. 54:1995;190-202.
20. Scharlau W. Quadratic and Hermitian Forms. Grundlehren der Mathematischen Wissenschaften. 1985;Springer-Verlag, New York/Berlin.
21. Schur I. Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen. Schur I. Gesammelte Abhandlungen I. 1973;198-250 Springer-Verlag, New York/Berlin.
22. Shioda T. Mordell-Weil lattices and Galois representations. Proc. Japan Acad. Ser. A. 65:1989;268-271.
23. Shioda T. Mordell-Weil lattices and sphere packings. Amer. J. Math. 113:1991;931-948.
24. Tiep P. H. Globally irreducible representations of finite groups and integral lattices. Geom. Dedicata. 64:1997;85-123.
25. Vignéras M.-F. Arithmétique des Algèbres de Quaternions. Lecture Notes in Mathematics. 1980;Springer-Verlag, New York/Berlin.
26. Washington L. C. Introduction to Cyclotomic Fields. Graduate Texts in Mathematics. 1982;Springer-Verlag, New York/Berlin.